In formulating past tenses of unlikely words or acronyms, an apostrophe-d is always used to prevent confusion or mispronunciation. (Obviously this is non-issue in speech.) You could also use the auxiliary do if you want to avoid this construction. These two sentences are thus correct:
- Only one person RSVP'd to my event.
- Only one person did RSVP to my event.
Also, keep in mind that whenever acronyms are put in past tense using the apostrophe-d formulation, no account is taken of the full logical meaning of the acronym. Thus, you have examples like
- DIY'd (which means engaged in a DIY project or carried out DIY on, etc),
- SWAK'd (sealed with a kiss),
and so forth.
RSVP (Répondez S'il Vous Plaît — reply if you please/please reply) is a special acronym because it functions as a verb. However, we have all found it convenient to take it away from its largely stiff, formal original context (e.g. RSVP: Mr. Jones) to more useful ones, such as:
- Don't forget to RSVP.
- I did not RSVP. Can I still come?
- Anyone planning to come should RSVP, so I know how many burgers to buy.
- Please RSVP ASAP! (never mind the repetition!)
The past tense is less common, but RSVP'd would be the correct way to write it down.